WO2020041068A1 - Perovskite nanocrystals and methods of making the same - Google Patents

Abstract

The present disclosure relates to a perovskite that includes A1-xA'xBX3, where A is a first cation, A' is a second cation, B is a third cation, X is a first anion, and 0 < x ≤ 1. In some embodiments of the present disclosure, the perovskite may further include a second anion (X') such that the perovskite includes A1-xA'xB(X1-zX'z)3, where 0 < z ≤ 1. In some embodiments of the present disclosure, the perovskite may further include a fourth cation (A*) such that the perovskite includes A1-x-yA'xA*yB(X1-zX'z)3, where 0 < y ≤ 1. In some embodiments of the present disclosure, the perovskite may further include a fifth cation (B') such that the perovskite includes A1-x-yA'xA*yB1-aB'a(X1-zX'z)3, where 0 < a ≤ 1.

Description

PEROVSKITE NANOCRYSTALS AND METHODS OF MAKING THE SAME

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S Provisional Patent Application No. 62/719,769 filed August 20^th, 2018, the contents of which are incorporated herein by reference in their entirety.

CONTRACTUAL ORIGIN

The United States Government has rights in this disclosure under Contract No. DE- AC36-08GO28308 between the United States Department of Energy and Alliance for Sustainable Energy, LLC, the Manager and Operator of the National Renewable Energy Laboratory.

BACKGROUND

The mixed A-cation composition of Csi-xFAxPbU is used in various reports of perovskite based optoelectronic devices (such as solar cells, light emitting materials, lasers, detectors, etc.) and reported in one instance in perovskite nanocrystals (NCs). However, in all of these reports, the full composition space with x varying from 0 to 1 has not been realized; e.g. x is limited to values less than 0.5. In thin films, the annealing temperature used to crystalize compositions with greater than 50% Cs (l-x>0.5) causes thermal decomposition of the FA (formamidinium). In direct synthesis of mixed composition nanocrystals, the reactivity of the Cs versus FA precursor differs enough to not allow for the full compositional tuning. Thus, there remains a need for new synthetic methods that enable the production of novel mixed cation perovskite compositions, having unique physical properties and characteristics.

SUMMARY

An aspect of the present disclosure is a perovskite that includes Ai-xA’xEDG, where A is a first cation, A’ is a second cation, B is a third cation, X is a first anion, and 0 < x < 1. In some embodiments of the present disclosure, the perovskite may further include a second anion (X’) such that the perovskite includes Ai-xA’xB(Xi-_zX’z)3, where 0 < z < l. In some embodiments of the present disclosure, the perovskite may further include a fourth cation (A*) such that the perovskite includes Ai-x-_yA’xA*_yB(Xi-zX’z)3, where 0 < y £ 1. In some embodiments of the present disclosure, the perovskite may further include a fifth cation (B’) such that the perovskite includes Ai-x-_yA’xA*_yBi-_aB’a(Xi-zX’z)3, where 0 < a < 1. In some embodiments of the present disclosure, each of A, A’, and A* may include at least one of an organic cation and/or an inorganic cation. In some embodiments of the present disclosure, each of A, A’, and A* may include at least one of a Group 1 Element, an alkylammonium, and/or formamidinium (FA). In some embodiments of the present disclosure, the alkylammonium may be methylammonium (MA). In some embodiments of the present disclosure, both B and B’ may include at least one of a Group 13 Element, a Group 14 Element, a Group 15 element, and/or a transition metal. In some embodiments of the present disclosure, both X and X’ may include a halogen.

In some embodiments of the present disclosure, the perovskite may include Csi-x-yFAxMA_yPb(Ii-zBrz)3. In some embodiments of the present disclosure, the perovskite may include at least one of Csi-_yMA_yPb(Ii-zBr_z)3, Csi-xFAxPb(Ii-zBr_z)3, and/or FAi-_yMA_yPb(Ii- zBr_z)3. In some embodiments of the present disclosure, the perovskite may include at least one of Cs i-yMAyPbh. Csi-xFAxPbB, FAi-yMAyPbB, Csi-_yMA_yPbBr3, Csi-xFAxPbBn, and/or FAi-_yMAyPbBr3.

An aspect of the present disclosure is a method that includes combining a first perovskite and a second perovskite, where the first perovskite has a first composition that includes a first cation (A), a second cation (B), and a first anion (X), the second perovskite has a second composition that includes a third cation (A’), a fourth cation (B’), and a second anion (X’), and the combining results in the forming of a third perovskite having a third composition that includes at least three of A, A’, B, B’, X, and/or X’. In some embodiments of the present disclosure, the first composition may include at least one of ABX3, A2BX6, and/or A3B2X9. In some embodiments of the present disclosure, the second composition may include at least one of A’B’X’3, A’₂B’X’6, and/or A’sB^XY

In some embodiments of the present disclosure, the third perovskite composition may include at least one of A”B”X”3, A”2B”X”6, and/or A”3B”2X”9, A” may include at least one of A and/or A’, B” may include at least one of B and/or B’, and X” may include at least one of X and/or X’. In some embodiments of the present disclosure, the first perovskite may include a least one of Cs2BiAgCl6, Cs2CuBil6, Cs2Pbl6, Cs2Snl6, Cs3Sb2l9, FAPbE, CsPbE, MAPbE, and/or MAPbBn,

In some embodiments of the present disclosure, the second perovskite may include a least one of Cs2BiAgCl6, Cs2CuBil6, Cs2Pbl6, Cs2Snl6, Cs3Sb2l9, FAPbE, CsPbE, MAPbE, and/or MAPbBn. In some embodiments of the present disclosure, the first perovskite may be different than the second perovskite. In some embodiments of the present disclosure, the third perovskite may include Csi-xFA_xPb(Ii-yBr_y)3, 0 < x < 1, and 0 < y < 1. In some embodiments of the present disclosure, 0.5 < x < 0.99. In some embodiments of the present disclosure, the first perovskite and the second perovskite may be provided at a molar ratio of the first perovskite to the second perovskite between 0.1 to 1.0 and 10 to 1.0.

BRIEF DESCRIPTION OF THE DRAWINGS

Some embodiments are illustrated in referenced figures of the drawings. It is intended that the embodiments and figures disclosed herein are to be considered illustrative rather than limiting.

Figures 1A, 1B, and 1C illustrate a crystal structure for a perovskite, according to some embodiments of the present disclosure.

Figure 2 illustrates a method for producing a perovskite having mixed A-cations, according to some embodiments of the present disclosure.

Figure 3A illustrates a schematic of an ion exchange of A-cations, Cs⁺ and FA⁺ ions between CsPbh and FAPbh nanocrystals (NCs), to form phase stable Csi-xFAxPbh NCs, according to some embodiments of the present disclosure.

Figure 3B illustrates the photoluminescence (PL) emission spectra depicting how CsPbh and FAPbh NCs convert into mixed cation NCs, according to some embodiments of the present disclosure. The dashed curve indicates the emission profile of one of the early stages of combining/forming a mixed perovskite.

Figures 4A through 4D illustrate optical properties and transmission electron microscopy (TEM) characterization of the Csi-xFAxPbh NCs, according to some embodiments of the present disclosure. Figure 4A illustrates ultraviolet- visible (UV-Vis) absorption spectra. Figure 4B illustrates PL emission spectra of the mixed NCs showing tunability over a range between about 650 nm and about 800nm range. Figure 4C illustrates a TEM image of Cso.5FAo.5Pbh NCs. Figure 4D illustrates photoluminescence excitation (PLE) spectra of Cso.5FAo.5Pbh NCs at different emission energies, which show the absence of substantial inhomogeneous broadening of the PL emission due to the mixed cation compositions.

Figure 5 illustrates the PL decay-profiles of starting and mixed cation NCs, integrated over the wavelength range studied, according to some embodiments of the present disclosure.

Figure 6 illustrates TEM images of NCs, according to some embodiments of the present disclosure: High resolution and low resolution TEM images of (Panels A and B) CsPbU NCs; (Panels C and D) FAPbL· NCs; (Panels E and F) Cso.75FAo.25PbU NCs; (Panels G and H) Cso.5FAo.5PbU NCs; and (Panels I and J) Cso.25FAo.75PbU NCs.

Figures 7A through 7D illustrate mixing of cations between different sized starting nanocrystals (smaller CsPbh and larger FAPbh NCs), according to some embodiments of the present disclosure: Figure 7A illustrates UV-Vis absorption and Figure 7B illustrates PL emission spectra of small CsPbh, large FAPbh and the resulting mixed cation perovskite NCs. Two kinds of distributions in the absorption spectrum of the mixed cation NCs are indicated by the vertical arrows in Figure 7A. Figure 7C illustrates the deconvolution of the asymmetric PL emission of the mixed A-cation Csi-_xFA_xPbh NCs; the spectrum can be deconvoluted with two Gaussians with peak maximum at ~680nm and ~728nm. Figure 7D illustrates PLE spectra collected at different emission wavelengths of the Csi-_xFA_xPbh NCs showing two different sets with two different transition energies. The corresponding emission position are indicated by the vertical arrows on the PL spectrum.

Figure 8A illustrates PLE spectra of mixed A-cation Cso.25FAo.75Pbh NCs, according to some embodiments of the present disclosure.

Figure 8B illustrates PLE spectra of mixed A-cation Cso.75FAo.25Pbh NCs, according to some embodiments of the present disclosure.

Figures 9A and 9B illustrate UV-Vis absorption and PL spectra, respectively, of the freshly prepared Csi-_xFA_xPbh NCs, according to some embodiments of the present disclosure.

Figures 9C and 9D illustrate UV-Vis absorption and PL spectra, respectively, of the same Csi- _xFA_xPbh NCs but two months after synthesis, according to some embodiments of the present disclosure.

Figure 10A illustrates x-ray diffraction (XRD) results of the Csi-_xFA_xPbl3 NCs, according to some embodiments of the present disclosure. (Panel A) illustrates wide-angle XRD patterns of the mixed cation NCs showing that the NCs retain their comer-sharing perovskite phase after forming mixed cation perovskites. The diffraction peaks for the FAPbU NCs were indexed following methods known in the field. (Panel B) illustrates a zoomed-in view of the (001) diffraction peak showing continuous shift from pure FAPbU to pure CsPbU.

Figure 10B illustrates Vegard’s law demonstrated by showing the linear shift the dooi peak with composition. Figure 11A illustrates a comparison of powder XRD of the CsPbL NCs (top trace) with standard reported bulk patterns (bottom traces), according to some embodiments of the present disclosure.

Figure 11B illustrates a comparison of powder XRD of the FAPbL NCs (top trace) with standard reported bulk patterns (bottom traces), according to some embodiments of the present disclosure.

Figure 12A illustrates the variation of the PL emission spectra as a function with composition of mixed A-cation Csi-xFAxPbL NCs, according to some embodiments of the present disclosure.

Figure 12B illustrates the variation of emission wavelength spectra as a function of composition of mixed A-cation Csi-xFAxPbL NCs, according to some embodiments of the present disclosure.

Figure 12C illustrates the variation of emission energies as a function of composition of mixed A-cation Csi-xFAxPbL NCs, according to some embodiments of the present disclosure.

Figure 13 A, 13B, and 13C illustrate the evolution of PL emission peaks with time at reaction temperatures of 45 °C, 70 °C, and 90 °C, respectively; the bottom-most spectra in these three figures show individual emission from CsPbL (labeled CPI) and FAPbL (labeled FAPI). The next two spectra (labeled“xmin_RT” where x is 2, 30, 38, and 40) are emissions at room temperature showing relatively stable peak positions. The remainder of the emission spectra are shown for the temporal evolution at elevated temperatures as labeled.

Figure 13D illustrates the shift in emission energy from their original position, depicting how the high energy peak (Ei) is red-shifting from pure CsPbL due to incorporation of FA⁺ and how the low-energy peak (E2) is blue-shifting from pure FAPbL due to incorporation of Cs⁺ over time. The dotted lines are exponential fits to the experimental data.

Figure 13E illustrates an Arrhenius plot showing the rates of conversion of CsPbL ( ki , bottom panel) and FAPbL (fe, top panel) into Csi-xFAxPbL against l/T (T being the absolute temperature). The dotted lines are linear fits to extract the activation energies (Iΰ IJ and E_a(2), respectively) for these processes.

Figures 14A through 14E illustrate the temperature kinetics of A-cation exchange at 45 °C, 60 °C, 70 °C, 80 °C, and 90 °C, respectively, according to some embodiments of the present disclosure. Figure 15 A illustrates the time dependent emission energies at different temperatures extracted from Gaussian fittings of the PL emission spectra shown in Figures 14A through 14E.

Figure 15B illustrates the shift in emission energies from their original position, depicting how the high energy peak is red-shifting from pure CsPbh due to incorporation of FA⁺ and how the low-energy peak is blue-shifting from pure FAPbh due to incorporation of Cs⁺. The dotted lines are exponential fitting to the experimental data.

Figure 16A illustrates a photograph of a solar cell device (Panel A) that includes an active layer composed of pure phase FAPbh NCs and CsPbh NCs as well as three compositions of the mixed A-cation perovskite NCs, and the corresponding cross-sectional scanning electron microscopy (SEM) image (Panel B) displaying solar cell architecture and typical layer thicknesses, according to some embodiments of the present disclosure.

Figure 16B illustrates J-V curves for Csi-xFAxPbh NC devices; bottom to top: pure FAPbh, Cso.25FAo.75Pbh, Cso.soFAo.soPbh, Cso.75FAo.25Pbh, pure CsPbh; the solid and dotted lines represent reverse and forward scans respectively; the solid squares on the J-V curves shows the SPO values, according to some embodiments of the present disclosure.

Figure 16C illustrates normalized EQE scans for each composition of Figure 16B, showing the tunable onset position depending on the NC composition, according to some embodiments of the present disclosure.

Figure 17A illustrates experimental Foe’s the voltage loss in the perovskite NC and thin film devices, according to some embodiments of the present disclosure.

Figure 17B illustrate the percentage fraction of observed Voc against the maximum attainable Voc as functions of band gap EG. The numbers beside the solid and open circles represent the x in the Csi-_xFA_xPbh perovskite NCs.

Figure 18A illustrates the voltage loss in the perovskite NC and thin film devices by plotting Voc, according to some embodiments of the present disclosure.

Figure 18B illustrates the percentage fraction of observed Voc against the maximum attainable Voc as functions of x in the composition of Csi-_xFA_xPbL perovskite NC devices, according to some embodiments of the present disclosure.

Figure 19A illustrates J-V scans of Csi-_xFA_xPbL perovskite thin film devices, according to some embodiments of the present disclosure.

Figure 19B illustrates normalized EQE spectra of Csi-_xFA_xPbL perovskite thin film devices, according to some embodiments of the present disclosure.

Figure 20 illustrates photoluminescence emission spectra of the Csi-xFAxPbBn-zL nanocrystals, according to some embodiments of the present disclosure.

Figure 21 illustrates UV-Vis absorption spectra of the Csi-xFAxPbL thin films with composition manipulated used ion exchange fromNCs, according to some embodiments of the present disclosure.

Figure 22A illustrates two-dimensional spectrotemporal TRPL data of CsPbh QDs, measured using a streak-camera. The dashed rectangle represents the portion of the trace that was integrated to construct an intensity versus decay -time transient.

Figure 22B illustrates TRPL transients of CsPb(Ii-_xBr_x)3, FAPb(Ii-_xBr_x)3 and FAi-xCs_xPb(Ii- xBr_x)3 colloidal QDs with bandgap energies of ca. 1.9 eV, according to some embodiments of the present disclosure.

Figure 22C illustrates PL lifetime versus bandgap of all colloidal QD samples including CsPb(Ii-xBr_x)3, FAPb(Ii-xBr_x)3, and FAi-xCsxPb(Ii-xBr_x)3 QDs, according to some embodiments of the present disclosure.

Figures 23A illustrates the optical absorbance of the various (Csi-x-yMA_xFA_y)Pbl3 NCs, according to some embodiments of the present disclosure.

Figure 23B illustrates the photoluminescence of the various (Csi-x-_yMA_xFA_y)Pbl3 NCs, according to some embodiments of the present disclosure.

Figure 23C illustrates x-ray diffraction data of MAPI nanocrystals. The bottom two traces are reference spectra.

Figures 24A, 24B, and 24C illustrate voltage-current plots of three photovoltaic devices that include an active layer made of two layers of nanocrystals, CsPbL, MAPbL, FA0.33MA0.33CS0.33PM3, respectively, according to some embodiments of the present disclosure.

REFERENCE NUMBERS

100. perovskite

110. A-cation

120. B-cation

130. X-anion

200. method 210. synthesizing a first starting perovskite

220. synthesizing a second starting perovskite

230. combining the first and second perovskite

240. forming a mixed perovskite

250. separating of the mixed perovskite

DETAILED DESCRIPTION

The present disclosure may address one or more of the problems and deficiencies of the prior art discussed above. However, it is contemplated that some embodiments as disclosed herein may prove useful in addressing other problems and deficiencies in a number of technical areas. Therefore, the embodiments described herein should not necessarily be construed as limited to addressing any of the particular problems or deficiencies discussed herein.

References in the specification to“one embodiment”,“an embodiment”,“an example embodiment”,“some embodiments”, etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.

As used herein the term“substantially” is used to indicate that exact values are not necessarily attainable. By way of example, one of ordinary skill in the art will understand that in some chemical reactions 100% conversion of a reactant is possible, yet unlikely. Most of a reactant may be converted to a product and conversion of the reactant may asymptotically approach 100% conversion. So, although from a practical perspective 100% of the reactant is converted, from a technical perspective, a small and sometimes difficult to define amount remains. For this example of a chemical reactant, that amount may be relatively easily defined by the detection limits of the instrument used to test for it. However, in many cases, this amount may not be easily defined, hence the use of the term“substantially”. In some embodiments of the present invention, the term“substantially” is defined as approaching a specific numeric value or target to within 20%, 15%, 10%, 5%, or within 1% of the value or target. In further embodiments of the present invention, the term“substantially” is defined as approaching a specific numeric value or target to within 1%, 0.9%, 0.8%, 0.7%, 0.6%, 0.5%, 0.4%, 0.3%, 0.2%, or 0.1% of the value or target. As used herein, the term“about” is used to indicate that exact values are not necessarily attainable. Therefore, the term“about” is used to indicate this uncertainty limit. In some embodiments of the present invention, the term“about” is used to indicate an uncertainty limit of less than or equal to ±20%, ±15%, ±10%, ±5%, or ±1% of a specific numeric value or target. In some embodiments of the present invention, the term“about” is used to indicate an uncertainty limit of less than or equal to ±1%, ±0.9%, ±0.8%, ±0.7%, ±0.6%, ±0.5%, ±0.4%, ±0.3%, ±0.2%, or ±0.1% of a specific numeric value or target.

The present disclosure relates to a process for creating a new class of perovskites, e.g. nanocrystals, crystals, and/or films, for example lead halide perovskites, for solar cells that exhibit high open circuit voltages (V_oc) with very low loss as compared to similar kinds of thin film perovskite photovoltaic devices. The process involves the synthesis of two or more different compositions of perovskite nanocrystals. The two or more compositions are then mixed together in suspension in varying relative amounts and then heated, resulting in a homogeneous perovskite composition made up of a mixture of the starting compositions. In some embodiments of the present disclosure, the nanocrystals may be an alloyed (i.e. formed) composition useful for various applications in optoelectronic devices including solar cells.

As described herein, some of these new perovskites were implemented into solar cell devices that generated up to about 90% of the maximum achievable Voc (as defined by the thermodynamic limit for a single junction solar cell). Exemplary perovskite compositions were created by combining at least one of methylammonium lead triiodide (MAPbE), formamidinium lead triiodide (FAPbh) and/or formamidinium lead tribromide (FAPbBn) with cesium lead triiodide (CsPbh) or cesium lead triiodide (CsPbBn) to create double A-cation (e.g. Cs and FA) perovskites, Csi-xFA_xPb(Ii-xBr_x)3, where perovskite compositions comprising the full range of x were produced (0 < x < 1), or triple A-cation (e.g. Cs, FA, and MA) perovskites were produced, Csi-x-yFAxMAyPbB, with 0 < x < 1 and 0 < y < 1. Some of the mixed perovskites (containing more than one A-cation or more than one A-cation and more than one X-anion) produced demonstrated bright and finely tunable emission in the red/near- infrared range between 650 nm and 800 nm. The activation energy for the miscibility between Cs⁺ and FA⁺ was measured and determined to be about 0.65 eV.

Although the present disclosure describes methods for producing novel compositions of Csi-xFAxPbE, Csi-_xFAxPb(Ii-xBr_x)3, and/or Csi-x-yFAxMAyPbE having mixed A-cations (e.g. Cs, MA, FA) or mixed A-cations and mixed X-anions (e.g. I and Br), the methods are believed to be applicable to a wide range of mixed-cation perovskites, as described below. In some embodiments of the present disclosure, the perovskite nanocrystals may exhibit quantum confinement effects; e.g. their bandgap and/or other optoelectronic and structural properties (photoluminescence lifetime, lattice constant, for example) may vary with nanocrystal size. In some embodiments of the present disclosure, a perovskite nanocrystal may have a characteristic length between one nanometer and one micrometer.

Figures 1A, 1B, and 1C illustrate that perovskites 100, for example halide perovskites, may organize into cubic crystalline structures with comer-sharing octahedra, as well as other crystalline structures such as tetragonal, hexagonal, and orthorhombic with either edge- or face sharing octahedra, and may be described by the general formula ABX3, where X (130) is an anion and A (110) and B (120) are cations, typically of different sizes (A typically larger than B). Figure 1A illustrates that a perovskite 100 may be organized into eight octahedra surrounding a central A-cation 110, where each octahedra is formed by six X-anions 130 surrounding a central B-cation 120. Figure 1B illustrates that a perovskite 100 may be visualized as a cubic unit cell, where the B-cation 120 is positioned at the center of the cube, an A-cation 110 is positioned at each comer of the cube, and an X-anion 130 is face-centered on each face of the cube. Figure 1C illustrates that a perovskite 100 may also be visualized as a cubic unit cell, where the B-cation 120 resides at the eight comers of a cube, while the A- cation 110 is located at the center of the cube and with 12 X-anions centrally located between B-cations along each edge of the unit cell.

For both unit cells illustrated in Figures 1B and 1C, the A-cations 110, the B-cations 120, and the X-anions 130 balance to the general formula ABX3, after accounting for the fractions of each atom shared with neighboring unit cells. For example, referring to Figure 1B, the single B-cation 120 atom is not shared with any of the neighboring unit cells. However, each of the six A-anions 130 is shared between two unit cells, and each of the eight A-cations 110 is shared between eight unit cells. So, for the unit cell shown in Figure 1B, the stoichiometry simplifies to B = 1, A = 8*0.124 = 1, and X = 6*0.5=3, or ABX3. Similarly, referring again to Figure 1C, since the A-cation is centrally positioned, it is not shared with any of the unit cells neighbors. However, each of the 12 X-anions 130 is shared between four neighboring unit cells, and each of the eight B-cations 120 is shared between eight neighboring unit cells, resulting in A = 1, B = 8 *0.125 = 1, and X = 12*0.25 = 3, or ABX3. Referring again to Figure 1C, the X-anions 130 and the B-cations 120 are shown as aligned along an axis; e.g. where the angle at the X-anion 130 between two neighboring B-cations 120 is exactly 180 degrees, referred to herein as the tilt angle. However, a perovskite 100 may have a tilt angle not equal to 180 degrees. For example, some embodiments of the present disclosure may have a tilt angle between 153 and 180 degrees.

Typical inorganic perovskites include calcium titanium oxide (calcium titanate) minerals such as, for example, CaTiCb and SrTiCb. In some embodiments of the present invention, the A-cation 110 may include a nitrogen-containing organic compound such as an alkyl ammonium compound. The B-cation 120 may include a metal and the X-anion 130 may include a halogen. Additional examples for the A-cation 110 include organic cations and/or inorganic cations, for example Cs, Rb, K, Na, Li, and/or Fr. Organic A-cations 110 may be an alkyl ammonium cation, for example a C1-20 alkyl ammonium cation, a C1-6 alkyl ammonium cation, a C2-6 alkyl ammonium cation, a C1-5 alkyl ammonium cation, a C1-4 alkyl ammonium cation, a C1-3 alkyl ammonium cation, a C1-2 alkyl ammonium cation, and/or a Ci alkyl ammonium cation. Further examples of organic A-cations 110 include methylammonium (CFLNH³⁺), ethylammonium (CFLCFLNFL^, propylammonium (CH3CH2 CFLNFL^, butylammonium (CH3CH2 CEL CFLNFL^, formamidinium (NH2CH=NH2⁺), hydrazinium, acetylammonium, dimethylammonium, imidazolium, guanidinium and/or any other suitable nitrogen-containing or organic compound. In other examples, an A-cation 110 may include an alkylamine. Thus, an A-cation 110 may include an organic component with one or more amine groups. For example, an A-cation 110 may be an alkyl diamine halide such as formamidinium (CH(NH₂)₂). Thus, the A-cation 110 may include an organic constituent in combination with a nitrogen constituent. In some cases, the organic constituent may be an alkyl group such as straight-chain or branched saturated hydrocarbon group having from 1 to 20 carbon atoms. In some embodiments, an alkyl group may have from 1 to 6 carbon atoms. Examples of alkyl groups include methyl (Ci), ethyl (C2), n-propyl (C3), isopropyl (C3), n-butyl (C₄), tert-butyl (C₄), sec-butyl (C4), iso-butyl (C4), n-pentyl (C5), 3-pentanyl (C5), amyl (C5), neopentyl (C5), 3-methyl-2-butanyl (C5), tertiary amyl (C5), and n-hexyl (G,). Additional examples of alkyl groups include n-heptyl (C7), n-octyl (Cs) and the like.

Examples of metal B-cations 120 include, for example, lead, tin, germanium, and or any other 2+ valence state metal that can charge-balance the perovskite 100. Further examples include transition metals in the 2+ state such as Mn, Mg, Zn, Cd, and/or lanthanides such as Eu. B-cations may also include elements in the 3+ valence state, as described below, including for example, Bi, La, and/or Y. Examples for X-anions 130 include halogens: e.g. fluorine, chlorine, bromine, and/or iodine. In some cases, a halide perovskite may include more than one X-anion 130, for example pairs of halogens; chlorine and iodine, bromine and iodine, and/or any other suitable pairing of halogens. In other cases, the halide perovskite 100 may include two or more halogens of fluorine, chlorine, bromine, and/or iodine.

Thus, the A-cation 110, the B-cations 120, and X-anion 130 may be selected within the general formula of ABX3 to produce a wide variety of halide perovskites 100, including, for example, methylammonium lead triiodide (CFbNFbPbL·), and mixed halide perovskites such as CFFNFFPbh YCLY and CFFNFFPbh LBG_l. Thus, a halide perovskite 100 may have more than one halogen element, where the various halogen elements are present in non-integer quantities; e.g. x is not equal to 1, 2, or 3. In addition, halide perovskites, like other organic-inorganic perovskites, can form three-dimensional (3-D), two-dimensional (2-D), one-dimensional (l-D) or zero-dimensional (0-D) networks, possessing the same unit structure. As described herein, the A-cation 110 of a perovskite 100, may include one or more A-cations, for example, one or more of cesium, FA, MA, etc. Similarly, the B-cation 120 of a perovskite 100, may include one or more B-cations, for example, one or more of lead, tin, germanium, etc. Similarly, the anion 130 of a perovskite 100 may include one or more anions, for example, one or more halogens. Any combination is possible provided that the charges balance.

For example, a perovskite having the basic crystal structure illustrated in Figures 1A, 1B, and 1C in at least one of a cubic, orthorhombic, and/or tetragonal structure, may have other compositions resulting from the combination of the cations having various valence states in addition to the 2+ state and/or 1+ state described above for lead and alkyl ammonium cations; e.g. compositions other than AB²⁺X₃ (where A is one or more cations, or for a mixed perovskite where A is two or more cations). Thus, the methods described herein may be utilized to create novel mixed cation materials having the composition of a double perovskite (elpasolites), A₂B¹⁺B³⁺X6, with an example of such a composition being Cs2BiAgCl6 and Cs2CuBil6. Another example of a composition covered within the scope of the present disclosure is described by A₂B⁴⁺X6, for example CS2PW6 and Cs2Snl6. Yet another example is described by A₃B2³⁺X9, for example Cs₃Sb2l9. For each of these examples, A is one or more cations, or for a mixed perovskite, A is two or more cations. As used herein, the term“mixed perovskite” refers to a perovskite having at least two of at least one of an A-cation, a B-cation, and/or an X-anion; i.e. two or more A-cations, two or more B-cations, and/or two or more X-anions.

Figure 2 illustrates a method 200 for producing a perovskite 100, as described above, in particular, a mixed perovskite having more than one A-cation 110 and/or more than one A- cation 110 and more than one X-anion 130; e.g. AI-_XA’_XBX₃ and/or Ai-_xA’_xB(Xi-_yX’_y)₃, where 0 < x < 1 and 0 < y £ l . In some embodiments of the present disclosure, the method 200 may begin with the first synthesizing 210 of a first starting perovskite and the second synthesizing 220 of a second starting perovskite. In some embodiments of the present disclosure, the first starting perovskite may be defined by ABX3, for example, FAPbh or FAPbBn (where A = FA, B = Pb, and X = I or Br), and the second starting perovskite may be defined by A’BX’3, for example, CsPbL· or CsPbBn (where A’ = Cs, B = Pb, and X’ = I or Br). However, these compositions are presented for illustrative purposes, and any other combination of perovskites may be used and are considered within the scope of the present disclosure. The method 200 may then proceed with the combining 230 of the first starting perovskite and the second starting perovskite, where the combining 230 results in the forming of a mixed perovskite defined by AI-_XA’_XBX3 and/or Ai-xA’xB(Xi-_yX’_y)3, for example, Csi-xFAxPbL· and/or Csi-xFA_xPb(Ii-_yBr_y)3, where 0 < x < 1 and 0 <y £ l depend on the conditions of the combining 230 (e.g. temperature, time, and/or agitation) and the ratios of the first starting perovskite to the second starting perovskite. The method 200 may then proceed with the separating 250 of the mixed perovskite from any other components (e.g. solvents, residual ions, and/or ligands) that were present in the combining 230 to yield a relatively pure form of the mixed perovskite 100. Although Csi- xFAxPb(Ii-_yBr_y)3 is describe above, the methods described herein are applicable to other perovskite formulations as described above. In some embodiments of the present disclosure, an exchangeable A-cation may include at least one of Rb, K, Na, guanidinium, dimethylammonium, imidazolium, and/or hydrazinium. In some embodiments of the present disclosure, an exchangeable X-anion may include at least one of a halogen and/or SCN . Perovskites undergoing the exchange of an A-cation or an A-cation and an X-anion may include at least one of Ge, Sn, Bi, In, Sb, Cd, and/or Zn.

Although the examples provided above illustrate methods for making mixed perovskites containing two unique A-cations and/or mixed perovskites containing two unique A-cations and two unique X-anions, perovskites having more than two unique A-cations and/or perovskites having more than two unique A-cations and more than two unique X-anions fall within the scope of the present disclosure. For example, in some embodiments of the present disclosure, a method 200 may begin with synthesizing of two or more starting perovskites (only two synthesizing steps shown in Figure 2, 210 and 220), where the two or more starting perovskites provide at least three unique A-cations to produce a final mixed perovskite containing the at least three unique A-cations. In some embodiments of the present disclosure, the methods described herein may result in compositions defined by Ai-x-_yA’_xA”_yBX3 and/or Ai-x-_yA’_xA”_y B(Xi_-zX’z)3, where 0 < x < 1, 0 < y < 1, and 0 < z < 1, with specific examples including Csi-x-yFAxMAyPbL·, Csi-x-yFA_xMA_yPbBr3, Csi-x-yFAxMA_yPb(Ii-zBr_z)3.

For example, the combining 230 may include dispersing colloidal solutions of two or more starting perovskites as nanocrystals into a noncoordinating solvent such as at least one of octane, l-octadecene, toluene, and/or dichlorobenzene. In some embodiments of the present disclosure, the solution may contain a coordinating group such as butylamine, octylamine, and/or oleylamine. The two or more starting perovskites may be provided at different ratios or concentrations to produce the desired A-cation composition of two or more A-cations; e.g. where the first starting perovskite is present at a concentration between 1 wt% and 99 wt%, with at least one additional starting perovskite making up the remainder. The resultant mixture may be heated to a temperature between 15 °C and 200 °C to facilitate the exchange, where the upper limit is defined by the boiling point of the noncoordinating solvent being used. The combining 230 may be performed for a time period between one minute and 48 hours. In some embodiments of the present disclosure, the combining 230 may be performed at a pressure between a vacuum (less than 1 atmosphere of pressure) to elevated pressures significantly above atmospheric pressure (e.g. between 1 atm and 10 atm). The final mixed perovskite resulting from the method 200, may include a thin film, a plurality of nanocrystals, and/or a single crystal. In some embodiments of the present disclosure, the combining 230 and the forming 240 may occur substantially simultaneously in the same reaction vessel. In some embodiments of the present disclosure, the forming 240 may proceed over a period of time, for example between one minute and 48 hours, depending on the exchange kinetics, as defined by the combining/forming conditions; e.g. temperature, starting perovskite concentrations, etc. In some embodiments of the present disclosure the separating 250 of the mixed perovskite 100 may be completed by any suitable method (e.g. chromatography, filtration, and/or centrifugation). Agitation may be provided to insure complete mixing and improve mass transfer.

Thus, disclosed herein is the synthesis, by post-synthetic cation exchange, of AI-_XA’_XBX3 and/or Ai-xA’xB(Xi-_xX’x)3 colloidal mixed perovskite NCs, for example, Csi- xFAxPbL· and/or Csi-xFAxPb(Ii-xBr_x)3, where 0 < x < l.by For example, by combining colloidal solutions of CsPbh or CsPbBn NCs with FAPbh or FAPbBn NCs in appropriate proportions along with modest heating allows cross-exchange between the A-cations (as well as cross exchange of X-anions, if desired), resulting in unique mixed compositions (mixed A-cation perovskites, with or without mixed X-anions) that retain their crystallographic framework (as shown in Figure 3A). The methods described herein provide controllable and tunable emission in the -650-800 nm range, in lead iodide perovskite NCs by control of the A-cation composition only. For A-cation exchange only (no X-anion exchange), individual CsPbL· and FAPbL NCs were used as“precursors” to yield a homogeneous mixed perovskite NC solution via continuous A-cation exchange between them (see Figure 3B). Photoluminescence (PL) kinetics at various combining/forming temperatures reveal that the interchange process is slower than anion (X) exchange, and the activation energy related to this process is about 0.65 eV. The resultant mixed perovskite Csi-xFAxPbL NCs were incorporated into solar cell devices that demonstrated lower Voc deficits compared to large grain film-based devices of similar composition and EG. The Csi-xFAxPbL· NC devices also show low hysteresis and a power conversion efficiency of about 10%.

To obtain the mixed compositions of Csi-xFAxPbL, colloidal NCs of CsPbL and FAPbL were first synthesized using the hot-injection method. The individual colloidal solutions were then mixed in controlled ratios. As can be seen in Figures 4A and 4B, the absorption onset and the PL emission peak positions was continuously tuned from pure CsPbL to pure FAPbL within the range of -650-800 nm. The time-resolved photoluminescence measurements reveal multi-exponential PL decay behavior with average lifetimes in the range of 23-55 ns, with the FAPbL exhibiting the slowest decay (see Figure 5). The transmission electron microscope (TEM) images (see Figure 4C) show that the mixed perovskite NCs retained their original size and shape (see Figure 6). Further, when NCs of different sizes were combined (e.g. small CsPbL NCs with PL maximum at -660 nm and larger FAPbL NCs with PL maximum at -770 nm), asymmetric absorption was observed with a bimodal distribution of particles and an asymmetric PL emission spectrum that can be deconvoluted with two Gaussians curves with peak maximums at -680 nm and -728 nm (see Figure 7A, 7B, and 7C). This indicates that the NCs retained their original size, with the final composition tuned by the relative amounts of Cs to FA total ions.

Photoluminescence emission (PLE) spectroscopy was employed to examine the forming of mixed A-cation Csi-xFAxPbL NCs. Figure 4D shows the PL of the Cso.5FAo.5PbL NCs and corresponding PLE spectra collected at different emission energies as dictated by the arrows on the emission spectrum. The overlap of all of the PLE spectra indicate that they are independent of emission energies and there is no significant inhomogeneous broadening of the PL emission due to the forming of mixed cation perovskite NCs. PLE measurements on the other compositions also point to the absence of significant inhomogeneity mixed A-cation perovskites (see Figures 8A and 8B). On the other hand, the PLE spectra collected at different emission energies in case of the mixed composition NCs resulted from intentionally mixing smaller CsPbL· and bigger FAPbL· NCs, clearly shows two distinct transitions at -670 nm and -700 nm (see Figure 7D), indicating inhomogeneous perovskite compositions or two different homogeneous perovskite compositions with two different mean sizes. The mixed cation perovskite NCs retain their absorption and PL emission shape for months after the ion exchange procedure, indicating that the mixed cation perovskite NCs reached thermodynamic equilibrium (see Figures 9 A - 9D).

Panel A of Figure 10A shows the powder XRD patterns of the mixed cation perovskite NCs. As can be seen from the XRD patterns, all of the mixed cation perovskite compositions retained their perovskite structure with prominent (001) and (002) peaks. The diffraction peaks shift monotonically between the patterns obtained with pure CsPbL and FAPbL NCs (see Panel B of Figure 10A) for zoomed in XRD pattern showing the shift of the (001) peak). CsPbL in bulk can have more than one perovskite phase with comer-shared octahedra. For example, neutron powder diffraction reveals that room temperature non-perovskite d-phase of CsPbL (orthorhombic, Pnma) can be converted into cubic a-phase (with undistorted comer shared [PbL]⁴ octahedra, Pm-3m) upon heating above 360 °C. There can be two more perovskite phases of CsPbL at temperatures lower than 360 °C depending upon the amount of tilting of the [PbL]⁴ octahedra: b-phase (260 °C) and g-phase (175 °C). These kinetically stabilized perovskite phases convert into the non-perovskite phase at room temperature in ambient conditions. On the other hand, FAPbL can exist in trigonal phase (space group P3ml) at room temperature, although it can also exist in the ideal cubic perovskite phase with space group Pm- 3m. As shown herein, powder X-Ray diffraction patterns were generated using reported crystallographic information to compare with the starting perovskites CsPbL and FAPbL NCs (see Figures 11 A and 11B). Both were stabilized in the perovskite phase at room temperature under ambient condition, although it is difficult to identify the exact amount of octahedral tilting and associated space group, due to Scherrer broadening of the XRD peaks.

To obtain a particular composition of Csi-_xFA_xPbL, it is important to know the starting concentration of CsPbL NCs and FAPbL NCs in the colloidal solution. However, this is not straightforward without knowledge of the size dependent molar extinction coefficient. While the size dependent molar extinction coefficient for CsPbBn NCs is known, similar studies on CsPbL and FAPbL have not been reported yet. However, the energy levels of valence band maxima and conduction band minima in lead halide perovskites are formed from lead and halide s and / atomic orbitals, and hence the density of states (DOS) near the band edges are expected to be similar for different APbXi perovskites if X is the same. So, it is reasonable to assume that colloidal solutions of similar sized CsPbL· and FAPbL· NCs with similar optical density near the band gap will have similar concentration of NCs in the component solutions. With this assumption, individual CsPbL· and FAPbL· NC solutions were prepared with similar absorbance near the band edge in different ratios. The XRD patterns and the PL emission spectra of all the compositions vary linearly with the presumed compositions (see Figures 10B, 12B, and 12C) validating the approximation of concentration.

In order to closely monitor the A-cation cross-exchange between CsPbL· and FAPbL· NCs, mixing the two was performed at various temperatures in a range between about 45 °C and 90 °C. Unlike the X-anion exchange, which occurs rapidly (timescale of two minutes), the A-cation exchange did not spontaneously occur at room temperature. The time-dependent PL measurements show that the two initial emission peaks merge into a single peak over time (the higher energy peak, referred to as Ei corresponds to the Cs-rich composition, and the lower energy peak, referred to as E2 corresponds to the FA-rich composition). As can be seen from Figures 13A, 13B, and 13C (also shown in Figures 14A - 14E), these two peaks did not move substantially from the original positions of CsPbL· and FAPbL· at room temperature at least up to ~40 minutes. The exchange was temperature dependent; the high energy and the low energy peaks merged more rapidly at elevated solution temperature. For example, referring to the PL emission spectral profile after 60 minutes at three different temperatures, the emission spectrum has two distinct peaks at 45 °C that have merged into a single peak at 90 °C. The emission energies of Ei and E2 over time are plotted in Figure 15 A. Assuming that the change in PL peak position is linear with respect to composition, then the rate at which these peaks shift from emission energies of pure CsPbL· and FAPbL· can be related to how fast Cs⁺ and FA⁺ ions leave the starting NC and diffuse into the other NC. It remains experimentally difficult to decouple and monitor these two processes separately. Nonetheless, it was observed that the rate of shift of the high energy (AEi) and the low energy peaks (A E2) can be reasonably fitted with single exponentials, indicating a first-order process, as shown in Figure 13D (see also Figure 15B). These rates can be used to extract the activation energy (E_a) related to the exchange (i.e. forming) process. Fitting these rates with the Arrhenius equation (see Figure 13E) yields an activation energy of -0.65 eV (see below for methods). This activation energy is higher than that reported for G diffusion in methylammonium and formamidinium lead iodide perovskites, or Br and Cl inter-diffusion in CsPbCl_xBri-_x nanowires (-0.45 eV).

Csi-_xFA_xPbL· NCs were used to fabricate photovoltaic devices with the device architecture shown in Figure 16A. There are several potential advantages to using perovskite NCs in photovoltaic devices over large grain perovskites. One main advantage is the phase stabilization of metastable perovskite phase of CsPbh. Secondly, ink for thin films is in the form of molecular precursors, and the homogeneity of the multi-crystalline absorber layer on the device depends on the substrate and other parameters like solvent evaporation, temperature, during crystallization. Using colloidal crystalline NC inks lifts the requirement of strict deposition conditions to control the film morphology, crystallinity and homogeneity. Formamidinium iodide (FAI) was used as a surface treatment to replace the long chain oleylammonium ligands. The devices show stabilized power output (SPO) efficiencies of -9- 11 % with low hysteresis and up to -75% external quantum efficiency (EQE) (see Figures 16B and 16C), and Table 1 below for a summary).

Table 1: Solar cell device parameters.

To directly compare the Voc of NC solar cells to the more traditional large grain perovskite devices, both types of solar cells were fabricated. The Voc for both perovskite NCs devices and large grain devices were compared as a function of the EG and of the A-cation composition (fraction of FA) and are shown in Figures 17A, 17B, 18A, and 18B. The Ac values were extracted from the onset of the EQE spectra. For the large grain devices, the A-cation composition was tuned with a Cs fraction of 0 to 0.3 because of the previously mentioned challenge in crystallization of compositions with higher amounts of Cs. A Voc up to -1.17V was obtained in the NC devices, as compared to just above 1.0V in bulk Csi-xFAxPbU devices. All of the thin film perovskite devices exhibited near state-of-the art Voc.

The quantum confinement effect in the NCs slightly increases EG of a particular composition, so it is more reasonable to compare the observed Voc to that of the thermodynamic limit for the determined EG (the dashed line in Figure 17 A). Voc Vor ^AX was plotted against EG in Figure 17B and against the fraction of FA in Figure 18B. Here, Voc is the observed open-circuit voltage, while Vor ^lx is the maximum available open-circuit voltage for a single junction solar cell with the given bandgap energy as determined by the Shockley- Queisser (SQ) theoretical analysis. This gives a comparative estimate of voltage loss in the devices. As seen in Figures 17A and 17B, the Voc loss is much less as compared to that of the bulk perovskite devices at any particular composition or bandgap value. Another important finding to note here is that although the pure FAPbh NC devices have somewhat lower efficiencies, they exhibited the lowest Voc loss at approximately 89% of the SQ limit.

Figure 20 illustrates two different perovskite nanocrystal solutions comprising ABX3 (where A=Cs, B=Pb and X=Br) and A’B’X’3 (where A=FA, B=Pb and X=I) were mixed at various ratios at 70 °C for 24 hours. The resultant Ai-_xA’xBi-yB’_yX3-zX’z NCs has emission ranging between ~5l0-780nm. Figure 21 illustrates another embodiment of the present disclosure, the exchange elements between a first perovskite in the form of nanocrystals to a second perovskite in the form of a thin film. In this example, an A’B’X’3 (where A=FA, B=Pb and X=I) bulk thin film on glass was dipped in a nanocrystal solution of ABX3 (where A=Cs, B=Pb and X=I) and heated at 70 °C for 24 hrs. The A’B’X’3 thin film transformed into mixed A-cation and X-anion compositions of Ai-xA’_xBi-yB’_yX3-zX’z as evidenced by a shift in the absorption spectra collected at different positions of the thin film.

As described above, in some embodiments of the present disclosure, mixed perovskite NCs may be synthesized that include both mixed A-cations and mixed X-anions, as defined by AI-_XA’_XB(XI-_XX’_X)3, for example, Csi-xFA_xPb(Ii-xBr_x)3, where 0 < x < 1. For example, CsPbBn and FAPbh QDs were synthesized using single-pot direct synthesis using controlled ratios of Pb-halide salts (see below for details). Then, the FAPbh and CsPbBn QD solutions were mixed at 70°C for 24 hours in a fixed Cs:FA molar ratio. To confirm the existence of single phase FAi-_xCsxPb(Ii-xBr_x)3 QDs, the resultant nanocrystals were characterized via photoluminescence emission and UV-Vis-NIR absorbance spectroscopy to ensure the convergence of the luminescence peak and first exciton.

Figure 22A shows two-dimensional TRPL data for CsPbh colloidal QDs, and the dashed box in Figure 22A shows the region of the response that is integrated to produce a TRPL transient decay curve. Figure 22B shows data for CsPb(Ii-_xBr_x)3, FAPb(Ii-_xBr_x)3, and FAi- _xCsxPb(Ii-xBr_x)3 colloidal QDs each with a composition tuned to achieve a bandgap of approximately 1.9 eV. The TRPL transients show that FA⁺ incorporation nearly doubles the lifetime from 29 ns to 55 ns for the FACs mixed composition sample or 64 ns for the sample with pure FA⁺ on the A-site. Thus, in this case, the A-cation mediated lengthening of the PL lifetime overrules X-anion mediated PL lifetime shortening. Figure 22C compares the intensity-weighted average PL lifetimes of the CsPb(Ii-_xBr_x)3, FAPb(Ii-_xBr_x)3, and FAi- _xCs_xPb(Ii-_xBr_x)3 QDs as a function of bandgap. The average lifetime of the CsPb(Ii-_xBr_x)3 QDs decreases significantly from about 45 ns to 15 ns across the compositional range, with a sharp decrease observed even for small bromide contents. In contrast, the FA-containing QDs appear to be less sensitive to the substitution of L with Br. Single-cation FAPb(Ii-_xBr_x)3 QDs exhibit similar lifetimes of >60 ns until the bandgap exceeds 1.8 eV (Br content of 42%) and then drops precipitously to 15 ns, similar to the average lifetimes observed for the single-cation Cs- containing QDs. The mixed-cation FAi_-xCs_xPb(Ii-_xBr_x)3 QDs, on the other hand, exhibit PL lifetimes that actually increase with bandgap energy, and reach 65 ns for a bandgap of 2.1 eV. This increase in PL lifetime with increasing bandgap for the FAi_-xCs_xPb(Ii-_xBr_x)3 composition appears to be unique among QDs.

In addition, the methods described herein may be employed to produce mixed perovskites having three or more unique A-cations as defined by Ai-_x-yA’_xA”_yBX3 and/or Ai-_x-yA’_xA”_y (Xi_-zX’z)3, where 0 < x < 1, 0 < y < 1, and 0 < z < 1, with specific examples including Csi-_x-yFA_xMA_yPbl3, Csi-_x-yFA_xMA_yPbBr3, Csi-_x-yFA_xMA_yPb(Ii-zBr_z)3. Figure 23A illustrates the optical absorbance of the various (Csi-_x-yMA_xFA_y)Pbl3 NCs. The dashed lines show the pure phase CsPbL (labeled CPI), CFLNFLPbL· (labeled MAPI), and CH(NH2)2PbL· (labeled FAPI). The solid lines show various NC compositions with mixed A- site composition. The onset of absorbance can be seen in the various samples to be tunable from 700 to 800 nm based on the A-site composition. Figure 23B illustrates the corresponding photoluminescence of these samples with peak emission wavelength tunable between 680 and 775 nm. Referring to Figure 23C, the x-ray diffraction data shows that MAPI nanocrystals exhibit a double at 2theta values of 23-24 confirming existence in the beta phase. The near equal peak heights of the peaks at 28 and 32 2theta also match the reference. In the NCs containing MA, FA and Cs cations, the peaks are closer in height than the NCs only containing FA and Cs. However, the doublet at 23-24 is harder to distinguish. The lower two traces are standard XRD patterns for reference.

Figures 24A, 24B, and 24C compare voltage-current plots of three photovoltaic devices having the general device structure of an active layer made of two layers of nanocrystals (Figure 24A - CsPbL, Figure 24B - MAPbL, and Figure 24C - FAo.33MAo.33Cso.33PbL·) positioned between a layer of TiC (acting as both an electron transfer layer and a first contact) and a hole transfer layer of Spiro-OMeTAD doped with lithium and 4-tert-butylpyridine (TBP). Positioned on the hole transfer layer was a second contact made of molybdenum oxide and aluminum. The triple A-cation perovskite NCs was produced according to the methods described above by mixing equal molar amounts of the three starting NC perovskites, CsPbh. MAPbh. and FAPbh. These results illustrate that the NCs are in the perovskite phase and function photovoltaically. The tables below summarize the performance metrics for each device. In some embodiments of the present disclosure, between each layer, the films were treated with MeOAc and after the film was deposited, an additional FAI (in MeOAc or ethylacetate) treatment was performed. Referring again to Figures 23 A -23C,“MeOAc” refers to experiments not using the FAI treatment (only the MeOAc treatment), whereas“FAI” refers to experiments using the FAI treatment (both the MeOAc and FAI treatments. Without wishing to be bound by theory, the MeOAc may replace oleate with acetate, and the FAI may remove residual oleylammonium ligands with FA ions.

Table 2: Device Stack Metrics using CsPbh NCs Active Layer

Table 3: Device Stack Metrics using MAPbh NCs Active Layer

Table 4: Device Stack Metrics using FAo.nMAo.nCso.nPbh NCs Active Layer

In conclusion, the examples above describe a methodology to synthesize colloidal Csi- xFAxPbh mixed composition NCs via a post-synthetic A-cation cation cross-exchange between CsPbh and FAPbh NCs. This method allows the synthesis of NCs with compositions that cannot be attained by direct synthesis, or in the bulk. The solar cell performance with these mixed composition perovskite NCs inks shows voltage approaching the SQ limit as compared to the bulk perovskite devices. This method, among other things, provides the opportunity to expand the library of tunable perovskite NCs via cation exchanges.

Methods:

Materials. Cesium Carbonate (CS2CO3; 99.9%), Oleic Acid (OA; technical grade, 90%), Oleylamine (OlAm; technical grade, 70%), l-Octadecene (l-ODE; technical grade, 90%), hexane (reagent grade, >95%), Octane (anhydrous, >99%), Methyl Acetate (MeOAc, anhydrous, 99.5%), Lead Nitrate (RMNOy. 99.999%), Ethyl Acetate (EtOAc, anhydrous, 99.8%), Cesium Iodide (Csl, 99.999%), Formamidinium Acetate (FA-acetate, 99%), Titanium Ethoxide (>97%), Hydrochloric Acid (HC1; 37% in water), Titanium diisopropoxide bis(acetylacetonate) (TAA, 75 wt% in iso-propanol), Chlorobenzene (anhydrous, 99.8%), Acetonitrile (anhydrous, 99.8%), Toluene (anhydrous, 99.8%), 4-tert-Butylpyridine (4-TBP; 96%), Dimethyl Formamide (DMF), Dimethyl Sulfoxide (DMSO) were purchased from Sigma-Aldrich. 2, 2', 7, 7'- tetrakis(N,N-di-p methoxyphenylamine)-9,9'-spirobifluorene (spiro- OMeTAD; >99.5% was purchased from Lumtec. Bis(trifluoromethane)sulfonimide lithium salt (Li-TFSI). Pbh (99.9985%) was purchased from Alfa Aesar. Formamidium Iodide (FAI), was purchased from Dyesol.

Synthesis of Cs-oleate precursor. 1.25 mmol (0.407 g) of CS2CO3, 20 ml l-ODE and 1.25 ml OA were loaded into 3-necked round bottom flask and degassed under vacuum at 60 °C for 30 minutes. The temperature was then increased to 150 °C under N2. Once the CS2CO3 reacted completely with the OA, the temperature was reduced to 120 °C and kept at this temperature for injection.

Synthesis of FA-oleate precursor. 5 mmol (0.521 g) of FA-acetate and 10 ml OA were loaded into 3-necked round bottom flask and degassed under vacuum at 50 °C for 30 minutes. The temperature was then increased to 120 °C under N2. Once the FA-acetate completely reacted to form a clear solution, the temperature was reduced to 80 °C and kept at this temperature for injection.

Synthesis of CsPbh NCs. CsPbh NCs were synthesized following methods known in the field. Briefly, 1.08 mmol (0.5 g) Pbh and 25 ml l-ODE were degassed under vacuum at 120 °C for 30 minutes inside a three-necked round bottom flask. A mixture of 2.5 ml OA and 2.5 ml OlAm, preheated to 120 °C, was injected into the reaction flask under vacuum. The mixture was briefly degassed until the Pbh dissolved to form a clear solution. Then the reaction mixture was heated to 180 °C under N₂ flow. At 180 °C, 2 ml of the Cs-oleate solution was quickly injected into the Pbh mixture, and the reaction mixture was immediately quenched in an ice- water bath. To separate the CsPbh NCs from the reaction liquor, 70 ml of MeOAc was added to the colloidal solution at room temperature and centrifuged at 7500 RPM for 5 minutes. The resulting precipitate was dispersed in 5 ml hexane, reprecipitated with 5 mL MeOAc and centrifuged again at 7500 RPM for 5 minutes. The resulting NCs were dispersed in 15 ml hexane and stored in the refrigerator until used. To prepare solutions for spin coating and cation exchange, the CsPbh NCs in hexane were removed from the refrigerator and centrifuged at 7500 for 5 minutes. The precipitate was discarded. The hexane from the supernatant was evaporated, and the NCs were finally redispersed in 1-2 ml of octane.

Synthesis of FAPbh NCs. The FAPbh NCs were synthesized following methods known in the field. Briefly, 0.74 mmol (0.344 g) Pbh and 20 ml l-ODE were degassed under vacuum at 120 °C for 30 minutes. A mixture of 4 ml OA and 2 ml OlAm, preheated to 120 °C was then injected into the Pbh mixture under vacuum. The mixture was briefly degassed under vacuum until the Pbh mixture became clear. Under N₂ flow, the temperature was reduced to 80 °C. At 80 °C, 5 ml of the FA-Oleate solution was swiftly injected into the Pbh mixture. After 5 seconds reaction time, the reaction mixture was quenched using an ice-water bath. After the mixture cooled to room temperature, 1 ml toluene and 5 ml MeOAc were added and the mixture was centrifuged at 8000 RPM for 30 mins. The resulting NC precipitate was dispersed in 7 ml toluene, reprecipitated with 5 mL MeOAc, and centrifuged at 8000 RPM for 10 minutes. The final precipitate was redispersed in 5-7 ml octane and stored under nitrogen for further use. The concentration of the FAPbh NCs was adjusted to be comparable to that of the CsPbh NC solution before synthesizing the mixed composition perovskites or fabricating devices.

Synthesis of Csi_-xFA_xPbh NCs. Colloidal solutions of CsPbh and FAPbh NCs dispersed in octane were mixed in different ratios to produce the desired Cs:FA stoichiometry. Before mixing, the absorption spectra of the individual samples were measured and the concentration was adjusted so that each solution had a similar optical density near the band edge. The mixture was either left to react for 48 hours at room temperature or reacted at different temperature (maximum 90 °C) for kinetics study.

Synthesis of CsPb(Ii_-xBr_x)₃ NCs. 1.08 mmol of PbX₂ powder (mixture of Pbh and PbBr₂) was dissolved in octadecene in a 3-neck flask. The mixture was subjected to a vacuum environment and heated to H0°C for 10 minutes. 2.5mL of oleylamine and 2.5 mL oleic acid were heated to l30°C and injected into the flask. This allows for dissolution of the lead salt; once the salt dissolves, the flask was subj ected to a nitrogen environment and the solution was heated to 185 °C. As soon as the solution temperature reached 185 °C, a Cs-oleate precursor, at 130 °C, was injected all at once into the flask. The Cs-oleate precursor was created by dissolving 407 mg of CS2CO3 in 20 mL of octadecene and 1.25 mL of oleic acid. Proper dissolution of the Cs- oleate required heating to 150 °C. Nucleation of CsPbX3 quantum dots occurs nearly instantaneously as the Cs-oleate is injected into the lead salt solution. In order to maintain relative mono-dispersity of the quantum dots, the flask was cooled to 25-30 °C in an ice bath immediately following injection of the Cs-oleate. Extra ligands were removed from the quantum dot solution by centrifuging with anhydrous methyl acetate for 5 minutes at 3500 RPM. Multiple washing steps were required to produce high yield product.

Synthesis of FAPb(Ii_-xBr_x)₃ NCs. 0.74 mmol of PbX₂ powder (mixture of Pbh and PbBn) were mixed in 25 mL of octadecene in a 3-neck flask. The mixture was degassed for 20 minutes at 120 °C. Separately, 4mL of oleic acid and 2mL of oleylamine were mixed at 130 °C for 20 min. The oleic acid/oleylammine mixture was then injected into the Pb-salt flask to dissolve the Pb-salt. Once dissolved, the flask atmosphere was changed to nitrogen and the temperature was adjusted to a targeted reaction temperature. FA-oleate precursor was prepared by mixing 521 mg of FA-acetate in 10-20 mL oleic acid in a 3-neck flask, yielding a FA concentration of 0.25-0.50 mM. This solution was then degassed at 50 °C for 20 minutes, after which, the temperature was increased to 120 °C to induce complete dissolution of the FA-oleate. Once dissolved, the atmosphere of the 3-neck flask was changed to nitrogen before the injection process. The reaction temperature for FAPb(Ii-_xBr_x)3 QDs varied from linearly 80 °C-l35 °C based on halide composition, with FAPbBn synthesis occurring at 135 °C and FAPbL at 80 °C. 5-10 mL of the FA-oleate precursor was rapidly injected into the PbX₂ solution at a targeted temperature and the reaction flask was quickly quenched in an ice bath. To remove excess ligands, the reacted QDs were taken into 3 mL of toluene and then subsequently crashed out of solution by adding 5 mL of methyl acetate to the toluene suspension and centrifuging at 8000 RPM for 30 minutes. The supernatant was discarded and the resulting pellet was dispersed in 7 mL of toluene. The toluene based QD solution was mixed with 5mL of methyl acetate and centrifuged at 8000 RPM for 10 minutes. The resulting supernatant was discarded and the pellet was dispersed in octane for use in characterization and device fabrication.

Synthesis of FAi_-xCs_xPb(Ii_-xBr_x)₃ NCs. First, FAPbL and CsPbBn QDs were synthesized using the methods outlined above. Then, FAPbh and CsPbBn QD solutions were mixed at 70°C for 24 hours in a fixed Cs:FA molar ratio. To confirm the existence of single phase FAi- _xCsxPb(Ii-xBr_x)3 QDs, the resultant nanocrystals were characterized via photoluminescence emission and UV-Vis-NIR absorbance spectroscopy to ensure the convergence of the luminescence peak and first exciton.

Characterization. UV-Vis absorption spectra were measured using a Shimadzu UV-3600 UV- VIS-NIR absorption spectrophotometer. Steady state PL emissions and PL excitation spectra were measured in a Horiba’s Fluoromax-4 emission spectrophotometer. TEM images were obtained on a FEI T30 electron microscope with 300 kV accelerating voltage. For the time- resolved PL measurements (TRPL), the samples were excited with a pulsed Fianium continuum laser source with an excitation of 450 nm and repetition rate of 1 MHz, and the emission spectra were collected using a Hamamatsu streak camera (Cl 0910-04). The XRD measurements were done on dropcast NC film using Rigaku’s DMax diffractometer with Cu-k_a radiation (wavelength 1.5406 A).

Perovskite NC Device Fabrication. All the solar devices were fabricated following methods known in the field. Briefly, a ~50 nm TiCh layer was deposited on patterned FTO coated glass substrate (Thin Film Devices, Inc.; pre-cleaned via sonication in iso-propanol, and then UV- Ozone treated for 10 minutes). The sol-gel TiCh was prepared by mixing 5 mL ethanol, 2 drops HC1, 125 pL deionized water, and 375 pL of titanium ethoxide, and stirred continuously for 48 hrs. The TiCh solution was filtered through a 0.20 pm polyvinylidene difluoride filter before use. The sol-gel TiCh was spin-cast on the FTO/glass substrate at 3000 RPM for 30 seconds, annealed at 450 °C for 30 minutes. 4 layers (-300 nm thick) of the NC absorber ink was then deposited layer-by-layer at 1000 RPM for 20 seconds followed by 2000 RPM for 5 seconds. The ligand exchange steps during the NC layer deposition involved dipping (for -1-2 seconds) of the device in saturated solution of Pb(NCh)2 in MeOAc (prepared by sonicating 20 mg Pb(NCh)2 in 20 ml MeOAc for -10 minutes, and then removing the excess salt by centrifuging at 3500 for 5 minutes) after each layer deposition followed by rinsing with neat MeOAc and dried immediately with a jet of dry air. After repeating these steps for 4-5 NC layers, the devices were finally soaked in a saturated solution of FAI in EtOAc (prepared by sonicating -20 mg FAI salt in -30 ml EtOAc for -15 minutes, and then removing the excess salt by centrifuging at 3500 for 5 minutes) for -10 seconds, followed by rinsing with neat MeOAc. The hole transporting materials was prepared by mixing 72.3mg of spiro-OMeTAD, 28.8 ml of 4-TBP, lml of chlorobenzene, and 17.5 ml of Li-TFSI stock solution (520 mg/ml in acetonitrile). The spiro-OMeTAD solution was then spincast on the NC absorber layer at 5000 RPM for 30 seconds. All deposition and ligand treatment procedures were performed in an ambient condition at relative humidity of -25-30%. The devices were left in the dry box overnight before depositing the top electrodes. MoOx was deposited at a rate of 0.1-0.5 A/s at a base pressure lower than 2* 10 ⁷ Torr for a total thickness of 15 nm. Aluminum electrodes were evaporated at a rate ranging from 0.5-2 A/s for a total thickness of 120 nm.

Perovskite Thin-fllm Device Fabrication. FAPbh thin-film devices were fabricated using methods known in the field. Briefly, a thin compact TiC layer with ~30nm thickness was first spin cast (700 RPM for 10 seconds, 1000 RPM for 10 seconds and 2000 RPM for 30 seconds) on cleaned, patterned, FTO-coated glass substrates from a 0.2M TAA solution in 1 -butanol. The TiC /FTO/glass substrate was then annealed at 130 °C for 5 minutes and at 450 °C for 60 minutes. A 0.7M stoichiometric FAI and PbL· solution in anhydrous DMF was prepared inside a glovebox and vortexed for 20 min at room temperature. The resulting clear, bright yellow solution was filtered through a 0.20 pm polyvinylidene difluoride filter and spin-cast inside a glovebox, on the compact TiC /FTO substrate by a consecutive three-step process: 500 RPM for 3 seconds, 3500 RPM for 10 seconds and 5000 RPM for 30 seconds. 1-2 seconds before the end of second step, a drop of toluene was gently placed on the spinning substrate. The resultant films were annealed at 170 °C for 1 min. For FA/Cs mixed perovskite compositions, absorber layers were deposited following methods known in the field. Briefly, inside a glove box, stoichiometric amounts of FAI, Csl and Pbh were dissolved in a mixed solvent of DMSO and DMF (v/v = 3/7) to obtain precursor solutions of Csi-xFAxPbL·. All the solutions were dissolved at room temperature by vortexing and they are filtered through 0.20 pm polyvinylidene difluoride filters before use. The solutions were then spincast on the TiCh/FTO/glass substrate using the following recipe: (1) 100 RPM for 3 seconds, (2) 3500 RPM for 10 seconds, (3) 5000 RPM for 30 seconds. During (3), after 20 seconds, 1 mL of toluene was deposited on the spinning substrate. The films were annealed at 170 °C for 10 min. Further layers, including spiro-OMeTAD deposition and the electrode depositions, were similar to that of the NC devices mentioned above except gold electrodes were deposited instead of aluminum electrodes. All the depositions were done inside a nitrogen filled glove box.

Device Characterizations. All the devices were tested using a Newport Oriel Sol3A solar simulator with a xenon lamp source inside a N2-filled glovebox. A KG5 filtered Si reference diode was used to calibrate the lamp intensity to 100 mW/cm² (AM1.5) and minimize the spectral mismatch of the lamp source. Devices were illuminated through a metal aperture (0.058 cm²). Stabilized power output was measured by holding the device at a constant voltage corresponding to the voltage at the maximum power point of a previous J-V scan. EQE measurements were taken using a Newport Oriel IQE200 system.

Calculation of Goldschmidt Tolerance Factor (GTF). The GTF’s for all the mixed A-cation compositions of Csi-xFAxPbL were calculated using the following formula:

where r, are the ionic radius of the individual species. The Shannon ionic radius for Cs⁺, Pb²⁺ and G were used, while reported effective radius for FA⁺ was used for the calculation: fcs = 188 pm, fpb = 119 pm, Gi = 220 pm, and TFA = 253 pm.

Determination of Activation Energy. To calculate the activation energy for the A-cation exchange, CsPbh and FAPbh nanocrystal solutions (1 : 1 ratio) were mixed at 45, 60, 70, 80 and 90 °C, and aliquots were taken at different time intervals for PL emission measurements. The PL emission spectra were then fitted with Gaussian functions to extract the peak emission energies. Before reaching a thermodynamically stable state with a single emission peak, the PL emission spectra of the intermediate aliquots could be resolved and fitted well with two Gaussians. The high energy peak (denoted LΊ) is indicative of high Cs-containing mixed A- cation perovskites and the low energy peak {Ei) is indicative of high FA-containing mixed A- cation perovskites in an ensemble of nanocrystals. The shift of E\ (DLΊ) and Ei (A Ei) from pure CsPbL and pure FAPbL emission positions, respectively, were found to be exponential as a function of time for all temperatures. The rate at which the emission energies (k) shift was extracted from exponential fitting. The activation energy, E_a, was then calculated using the Arrhenius equation:

or,

where, ks is the Boltzmann constant, T is the absolute temperature, andrio is the pre-exponential factor. Examples:

Example 1. A method comprising: combining a first perovskite and a second perovskite, wherein: the first perovskite has a first composition comprising a first cation (A), a second cation (B), and a first anion (X), the second perovskite has a second composition comprising a third cation (A’), a fourth cation (B’), and a second anion (X’), and the combining results in the forming of a third perovskite having a third composition comprising at least three of A, A’, B, B’, X, or X’.

Example 2. The method of Example 1, wherein the first composition comprises at least one of ABX3, A2BX6, or A3B2X9.

Example 3. The method of either Examples 1 or 2, wherein the second composition comprises at least one of A’B’X’3, A’2B’X’6, or A’3B’2X’9.

Example 4. The method of any one of Examples 1-3, wherein: the third perovskite composition comprises at least one of A”B”X”3, A”2B”X”6, or A”3B”2X”9, A” comprises at least one of A or A’, B” comprises at least one of B or B’, and X” comprises at least one of X or X’.

Example 5. The method of any one of Examples 1-4, wherein: the third perovskite composition comprises at least one of A”B”X”3, A”2B”X”6, or A”3B”2X”9, A” comprises A and A’, B” comprises at least one of B or B’, and X” comprises at least one of X or X’.

Example 6. The method of any one of Examples 1-5, wherein: the third perovskite composition comprises at least one of A”B”X”3, A”2B”X”6, or A”3B”2X”9, A” comprises A and A’, B” comprises at least one of B or B’, and X” comprises X and X’.

Example 7. The method of any one of Examples 1-6, wherein X comprises a halogen.

Example 8. The method of any one of Examples 1-7, wherein X’ comprises a halogen.

Example 9. The method of any one of Examples 1-8, wherein B comprises at least one of a

Group 13 Element, a Group 14 Element, a Group 9 element, or a transition metal.

Example 10. The method of any one of Examples 1-9, wherein B’ comprises at least one of a Group 13 Element, a Group 14 Element, a Group 15 element, or a transition metal.

Example 11. The method of any one of Examples 1-10, wherein A comprises at least one of an organic cation or an inorganic cation. Example 12. The method of any one of Examples 1-11, wherein A’ comprises at least one of an organic cation or an inorganic cation.

Example 13. The method of any one of Examples 1-12, wherein A comprises at least one of a Group 1 Element, an alkylammonium, or formamidinium (FA).

Example 14. The method of any one of Examples 1-13, wherein A’ comprises at least one of a Group 1 Element, an alkylammonium, or formamidinium (FA).

Example 15. The method of any one of Examples 1-14, wherein the alkylammonium is methylammonium (MA).

Example 16. The method of any one of Examples 1-15, wherein the alkylammonium is methylammonium (MA).

Example 17. The method of any one of Examples 1-16, wherein: the first perovskite comprises a least one of Cs2BiAgCl6, Cs2CuBil6, Cs2Pbl6, Cs2SnL·, Cs3Sb2l9, FAPbL·, CsPbL·, MAPbB. or MAPbBn, the second perovskite comprises a least one of Cs2BiAgCl6, Cs2CuBil6, Cs2Pbl6, Cs2Snl6, Cs3Sb2l9, FAPbB, CsPbB, MAPbB, or MAPbBn, the first perovskite is different than the second perovskite.

Example 18. The method of any one of Examples 1-17, wherein the first perovskite comprises CsPbB and the second perovskite comprises FAPbB.

Example 19. The method of any one of Examples 1-18, wherein the third perovskite comprises Csi-xFAxPbB, and 0 < x < 1.

Example 20. The method of any one of Examples 1-19, wherein 0.5 < x < 0.99.

Example 21. The method of any one of Examples 1-20, wherein the first perovskite comprises CsPbB or CsPbBn and the second perovskite comprises FAPbB or FAPbBn.

Example 22. The method of any one of Examples 1-21, wherein the third perovskite comprises Csi-xFAxPb(Ii-_yBr_y)3, 0 < x < 1, and 0 < y < 1.

Example 23. The method of any one of Examples 1-22, wherein 0.5 < x < 0.99.

Example 24. The method of any one of Examples 1-23, wherein: the second perovskite further comprises a fifth cation (A*), the third perovskite comprises Ai-x-_yA’_xA*_yBi-_aB’_a(Xi- zX’z)3, 0 < a £ l, 0 < b < l, 0 < x < l, 0 < y < l, and 0 < z < 1.

Example 25. The method of any one of Examples 1-24, wherein: a = 1 and the third perovskite comprises Ai-x-_yA’xA*_yB(Xi-_zX’z)3. Example 26. The method of any one of Examples 1-25, wherein: y = 1 and the third perovskite comprises AI-_XA’_XB(XI-ZX’Z)3.

Example 27. The method of any one of Examples 1-26, wherein: z = 1 and the third perovskite comprises AI_-XA’_XBX3.

Example 28. The method of any one of Examples 1-27, wherein the first perovskite and the second perovskite are provided at a molar ratio of the first perovskite to the second perovskite between 0.1 to 1.0 and 10 to 1.0.

Example 29. The method of any one of Examples 1-28, wherein the ratio is between 0.1 to 1.0 and 1.0 to 1.0.

Example 30. The method of any one of Examples 1-29, wherein the ratio is between 1.0 to 1.0 and 10 to 1.0.

Example 31. The method of any one of Examples 1-30, wherein the combining is performed at a temperature between 15 °C and 150 °C.

Example 32. The method of any one of Examples 1-31, wherein the combining is performed for a period of time between 1 hour and 24 hours.

Example 33. The method of any one of Examples 1-32, wherein at least one of the first perovskite or the second perovskite is in a colloidal solution.

Example 34. The method of any one of Examples 1-33, wherein at least one of the first perovskite or the second perovskite comprises a nanocrystal.

Example 35. The method of any one of Examples 1-34, wherein the third perovskite comprises a nanocrystal.

Example 36. The method of any one of Examples 1-35, wherein at least one of the first perovskite or the second perovskite is in the form of a first thin film.

Example 37. A perovskite comprising: AI_-XA’_XBX3, wherein: A is a first cation, A’ is a second cation, B is a third cation, X is a first anion, and 0 < x < 1.

Example 38. The perovskite of Example 37, further comprising: a second anion (X’) such that the perovskite comprises AI-_XA’_XB(XI-_ZX’_Z)3, wherein 0 < z < 1.

Example 39. The perovskite of either Examples 37 or 38, further comprising: a fourth cation (A*) such that the perovskite comprises Ai-_x-yA’_xA*_yB(Xi-zX’z)3, wherein 0 < y £ 1· Example 40. The perovskite of any one of Examples 37-39, further comprising: a fifth cation (B’) such that the perovskite comprises Ai-x-yA’xA*_yBi-aB’a(Xi-zX’z)3, wherein 0 < a < 1.

Example 41. The perovskite of any one of Examples 37-40, wherein A comprises at least one of an organic cation or an inorganic cation.

Example 42. The perovskite of any one of Examples 37-41, wherein A’ comprises at least one of an organic cation or an inorganic cation.

Example 43. The perovskite of any one of Examples 37-42, wherein A comprises at least one of a Group 1 Element, an alkylammonium, or formamidinium (FA).

Example 44. The perovskite of any one of Examples 37-43, wherein A’ comprises at least one of a Group 1 Element, an alkylammonium, or formamidinium (FA).

Example 45. The perovskite of any one of Examples 37-44, wherein the alkylammonium is methylammonium (MA).

Example 46. The perovskite of any one of Examples 37-45, wherein the alkylammonium is methylammonium (MA).

Example 47. The perovskite of any one of Examples 37-46, wherein A* comprises at least one of an organic cation or an inorganic cation.

Example 48. The perovskite of any one of Examples 37-47, wherein A* comprises at least one of a Group 1 Element, an alkylammonium, or formamidinium (FA).

Example 49. The perovskite of any one of Examples 37-48, wherein the alkylammonium is methylammonium (MA).

Example 50. The perovskite of any one of Examples 37-49, wherein B comprises at least one of a Group 13 Element, a Group 14 Element, a Group 15 element, or a transition metal.

Example 51. The perovskite of any one of Examples 37-50, wherein B’ comprises at least one of a Group 13 Element, a Group 14 Element, a Group 15 element, or a transition metal.

Example 52. The perovskite of any one of Examples 37-51, wherein X comprises a halogen.

Example 53. The perovskite of any one of Examples 37-52, wherein X’ comprises a halogen.

Example 54. The perovskite of any one of Examples 37-53 comprising Cs l -x-y F AxMAyP b(Ii-zBr_z)3. Example 55. The perovskite of any one of Examples 37-54 comprising at least one of Csi-_yMAyPb(Ii-zBr_z)3, Csi-xFA_xPb(Ii-zBr_z)3, or FAi-yMA_yPb(Ii-zBr_z)3.

Example 56. The perovskite of any one of Examples 37-55 comprising at least one of Csi-yMAyPbB, Csi-xFAxPbB, FAi-yMAyPbE, Csi-yMAyPbBn, Csi-xFAxPbBn, or FAi-yMAyPbBn.

The foregoing discussion and examples have been presented for purposes of illustration and description. The foregoing is not intended to limit the aspects, embodiments, or configurations to the form or forms disclosed herein. In the foregoing Detailed Description for example, various features of the aspects, embodiments, or configurations are grouped together in one or more embodiments, configurations, or aspects for the purpose of streamlining the disclosure. The features of the aspects, embodiments, or configurations, may be combined in alternate aspects, embodiments, or configurations other than those discussed above. This method of disclosure is not to be interpreted as reflecting an intention that the aspects, embodiments, or configurations require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects he in less than all features of a single foregoing disclosed embodiment, configuration, or aspect. While certain aspects of conventional technology have been discussed to facilitate disclosure of some embodiments of the present invention, the Applicants in no way disclaim these technical aspects, and it is contemplated that the claimed invention may encompass one or more of the conventional technical aspects discussed herein. Thus, the following claims are hereby incorporated into this Detailed Description, with each claim standing on its own as a separate aspect, embodiment, or configuration.

Claims

CLAIMS What is claimed is:

1. A perovskite comprising:

AI-_XA’_XBX3, wherein:

A is a first cation, A’ is a second cation, B is a third cation, X is a first anion, and 0 < x < 1.

2. The perovskite of claim 1, further comprising:

a second anion (X’) such that the perovskite comprises AI-_XA’_XB(XI-_ZX’_Z)3, wherein 0 < z < 1.

3. The perovskite of either claim 1 or 2, further comprising:

a fourth cation (A*) such that the perovskite comprises Ai-x-_yA’xA*_yB(Xi-zX’z)3, wherein 0 < y £ 1·

4. The perovskite of any one of claims 1-3, further comprising:

a fifth cation (B’) such that the perovskite comprises Ai-x-_yA’xA*_yBi-_aB’a(Xi-zX’z)3, wherein 0 < a < 1.

5. The perovskite of any one of claims 1-4, wherein each of A, A’, and A* comprises at least one of an organic cation or an inorganic cation.

6. The perovskite of any one of claims 1-5, wherein each of A, A’, and A* comprises at least one of a Group 1 Element, an alkylammonium, or formamidinium (FA).

7. The perovskite any one of claims 1-6, wherein the alkylammonium is

methylammonium (MA).

8. The perovskite any one of claims 1-7, wherein both B and B’ comprise at least one of a Group 13 Element, a Group 14 Element, a Group 15 element, or a transition metal.

9. The perovskite any one of claims 1-8, wherein both X and X’ comprise a halogen.

10. The perovskite any one of claims 1-9 comprising Csi-x-_yFAxMA_yPb(Ii-zBr_z)3.

11. The perovskite any one of claims 1-10 comprising at least one of Csi-_yMA_yPb(Ii- zBr_z)3, Csi-xFAxPb(Ii-zBr_z)3, or FAi-_yMA_yPb(Ii-zBrz)3.

12. The perovskite any one of claims 1-11 comprising at least one of Csi-vMA Pbh. Csi-xFAxPbL·, FAi-yMAyPbL·, Csi-yMAyPbBn, Csi-xFAxPbBn, or FAi-yMAyPbBn.

13. A method comprising:

combining a first perovskite and a second perovskite, wherein:

the first perovskite has a first composition comprising a first cation (A), a second cation (B), and a first anion (X),

the second perovskite has a second composition comprising a third cation (A’), a fourth cation (B’), and a second anion (X’), and

the combining results in the forming of a third perovskite having a third composition comprising at least three of A, A’, B, B’, X, or X’.

14. The method of claim 13, wherein the first composition comprises at least one of ABX₃, A₂BX₆, or A3B2X9.

15. The method of either claim 13 or 14, wherein the second composition comprises at least one of A’B’X’3, A^B’X’e, or AriB^XY